Assume the CAPM is the correct asset pricing model,and the risk-free rate of return is 6% and the market portfolio has an expected return and a standard deviation of 16% and 0.10%,respectively.An investor has a portfolio consisting of asset A,which has a beta of 1.6,and asset B,which has a beta of 0.6.If the investor wishes to earn a return identical to that of the market portfolio,what weight should the investor place in assets A and B?

A) $ 33 \% $ in asset $ \mathrm{A} $ and $ 67 \% $ in asset $ \mathrm{B} $
B) $ 40 \% $ in asset $ A $ and $ 60 \% $ in asset $ B $
C) $ 50 \% $ in asset $ A $ and $ 50 \% $ in asset $ B $
D) $ 60 \% $ in asset A and $ 40 \% $ in asset $ B $

Question

Assume the CAPM is the correct asset pricing model,and the risk-free rate of return is 6% and the market portfolio has an expected return and a standard deviation of 16% and 0.10%,respectively.An investor has a portfolio consisting of asset A,which has a beta of 1.6,and asset B,which has a beta of 0.6.If the investor wishes to earn a return identical to that of the market portfolio,what weight should the investor place in assets A and B?

A) $ 33 \% $ in asset $ \mathrm{A} $ and $ 67 \% $ in asset $ \mathrm{B} $
B) $ 40 \% $ in asset $ A $ and $ 60 \% $ in asset $ B $
C) $ 50 \% $ in asset $ A $ and $ 50 \% $ in asset $ B $
D) $ 60 \% $ in asset A and $ 40 \% $ in asset $ B $

Quizplus · Accepted Answer

To earn a return equal to the market portfolio,the portfolio must have the same risk as the market portfolio.In terms of the CAPM,that means the beta of the portfolio must be equal to 1.Using equation 8.4,and defining the weight in asset A as w_A,we know 1 = w_A(1.6)+ (1 - w_A)(0.6),which can be solved to obtain w_A = 0.40.Hence,w_B = 0.6.

Assume the CAPM Is the Correct Asset Pricing Model,and the Risk-Free